A Practical Application of Relativity to Observation and Control of ...

A Practical Application of Relativity to 

Observation and Control of MESSENGER 

Timekeeping 

INTRODUCTION 

The MErcury Surface, Space ENvironment, 

GEochemistry and Ranging (MESSENGER) mission 

timekeeping system provides accurate time information 

to both onboard and ground-based users of MESSENGER 

time. 1 In particular, it provides real-time estimates 

of time to the onboard guidance and control (G&C) 

subsystem, which needs knowledge of time to support 

the critical function of spacecraft attitude control. The 

accuracy of the timekeeping system, however, depends 

on the performance of the oscillator that is used to drive 

the onboard clock counter. That counter is called the 

mission elapsed time (MET) counter and records elapsed 

388 

Stanley B. Cooper 

he MESSENGER mission to Mercury, designed, implemented, and managed 

by The Applied Physics Laboratory, uses a partially automated timekeeping 

system to ensure that the knowledge of time is properly maintained 

onboard the spacecraft and on the ground. Since 2007, accurate time has been maintained 

when required through the use of a very stable oscillator. The behavior of that 

oscillator, and hence of the timekeeping system itself, has varied in flight in a manner 

that was not observed on the ground but which conforms to the special and general 

theories of relativity. Through accounting for the effects of relativity, we have been able 

to determine the rate of aging of the oscillator and are therefore able to predict the 

future behavior of the timekeeping system. This knowledge is now routinely applied by 

the MESSENGER Mission Operations Center to predict when new time parameters will 

need to be uploaded to the spacecraft as well as the values that need to be uploaded. 

time in terms of clock “ticks,” each such tick lasting 

approximately 1 ms. 

Time is provided to the G&C subsystem in two 

forms, namely, MET and Terrestrial Dynamical Time 

(abbreviated TDT or TT). Terrestrial Dynamical 

Time is a representation of time on the surface of the 

Earth and, for practical purposes, is equivalent to the 

commonly used UTC (Coordinated Universal Time). 

This estimate of Earth time is used by the G&C 

subsystem to determine where the spacecraft is in its 

orbit so that it can determine what the spacecraft 

attitude should be. 

JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 32, NUMBER 1 (2013)

The spacecraft actually contains four oscillators that 

can be used to support onboard timekeeping. The current 

configuration of the spacecraft avionics allows either 

of two of those oscillators to be used to drive the MET 

counter. One is a very stable oven-controlled crystal 

oscillator (OCXO) that is used to provide the timekeeping 

system accuracy required to support science observations. 

Owing to reliability concerns, however, the other 

less-stable “coarse” oscillator is used to drive the MET 

counter whenever an engine burn is performed. This has 

occurred numerous times—during cruise, during Mercury 

orbit insertion (MOI), and also at many solar perihelia 

and aphelia while the spacecraft is in orbit around 

Mercury. This occasional deselection of the “precision” 

oscillator, the OCXO, has produced numerous gaps in 

our record of OCXO performance. Even with those 

gaps, however, some very interesting and useful information 

has been gathered about the behavior of the OCXO 

and of the timekeeping system itself. 

The timekeeping system produces, on the ground, 

an estimate of the correlation between MET and Earth 

time in terms of the TT system. It saves that estimate 

in a text file called the Operations SCLK (Spacecraft 

Clock) Kernel. The SCLK Kernel estimate of clock 

behavior directly maps to average oscillator behavior. 

When the OCXO is selected, comparison of that average 

oscillator behavior to how we would predict the 

oscillator to behave according to the special and general 

theories of relativity provides us with knowledge of how 

much the OCXO behavior deviates from those predictions. 

Those “residuals” tell us how the physical OCXO 

actually behaves, as a local observer on the spacecraft 

would see it. Trending those residuals allows us to predict 

how the OCXO will behave in the future, and that 

prediction, in turn, is routinely used by the MESSEN- 

GER Mission Operations Center at APL to control the 

onboard real-time estimate 

of Earth time (TT) used by 

the G&C subsystem. 2 

The MESSENGER timekeeping 

system has not 

only provided us with the 

practical result of accurate 

onboard time for the G&C 

subsystem but has also provided 

a rare opportunity 

to have a glimpse, however 

small, into the theoretical 

universe of Albert Einstein. 

THE VENUS FLYBY IN 2007 

In early 2007, the MES- 

SENGER spacecraft began 

to use the oscillator designated 

OCXO-B to control 

the spacecraft clock. Shortly 

Frequency offset (clock drift rate) (ppb) 

35 

30 

25 

20 

15 

10 

5 

Actual MET drift rate 

Residual clock drift rate 

MET drift rate minus velocity effect 

afterward, the spacecraft had its second flyby of Venus 

to provide a gravity-assisted course correction on its 

long journey toward Mercury. The variation in OCXO 

behavior that was evident from the behavior of the MET 

counter as estimated in the Operations SCLK Kernel 

was much greater than we had seen during testing on 

the Earth and was much greater than could be explained 

by environmental factors such as the sensitivity of the 

OCXO output frequency to temperature variations. The 

explanation lies in the theory of relativity, which tells us 

that both velocity and gravity can measurably affect the 

observed behavior of a distant clock or oscillator. Time, 

according to the theory, is not the same for all observers. 

Observations during the 2 months after the OCXO 

was selected, including the closest approach to Venus 

during the second MESSENGER flyby of Venus, are 

illustrated in Fig. 1. The observed OCXO fractional 

frequency offset (bottom curve) varied by 11 parts per 

billion (ppb), much more than we had observed during 

ground testing. That is equivalent to a variation in the 

MET counter of 11 ns/s or 0.95 ms/day. This OCXO was 

custom designed to limit sensitivity to environmental 

factors and, for example, was designed to allow only 

4 ppb OCXO fractional frequency variation or 0.35 ms/ 

day over the full 40°C operational temperature range. 

Also, the oscillator experienced a temperature variation 

of only 4°C during the Venus flyby. The frequency 

changes that we observed were much greater than environmental 

variations could cause. 

Let’s focus first on the effect of velocity on the oscillator 

frequency performance. Special relativity tells us that 

time on the spacecraft (the MET counter) is related to the 

time perceived by a distant observer by the Lorentz factor 

= 1/ [1 − (v 2 /c 2 )] 0.5 , where c is the speed of light and v 

is the magnitude of the velocity of the spacecraft in the 

coordinate frame of the distant observer. Because oscil- 

0 960 970 980 990 1000 1010 1020 1030 1040 1050 

Days since launch 

Figure 1. Residual MESSENGER OCXO-B behavior after March 2007 turn-on. 

JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 32, NUMBER 1 (2013) 389

S. B. COOPER 

lator frequency and clock 

time are closely related, the 

Lorentz factor also describes 

how our observation of 

OCXO frequency is related 

to the oscillator frequency 

that would be seen by an 

observer traveling with 

the spacecraft. Subtracting 

this effect from our data, 

the bottom curve in Fig. 1, 

leads to the middle curve. 

All computations are with 

respect to the solar barycenter, 

that is, the velocity is 

the velocity of the spacecraft 

according to an observer at 

the solar barycenter. 

A particularly interesting 

feature of these curves 

is that the jump in OCXO 

fractional frequency offset that appears near the end 

of the observed data is absent from those data after 

removal of the relativistic velocity effect. That jump 

corresponds to the simultaneous reduction in velocity, 

shown in Fig. 2, which resulted from the close flyby of 

Venus. (The apparent time shift in the observed jump in 

OCXO frequency compared with the time of the jump 

in velocity is an artifact of the way the frequency jump 

was computed, but that detail is discussed later.) 

The general theory of relativity provides the tools for 

understanding how gravity affects the output frequency 

of the OCXO. The stronger the gravity field experienced 

by the oscillator, the slower that oscillator runs, at least 

as seen by a distant observer in a fixed gravity field. That 

behavior is described by 

the expression −(GM/c 2 )/R, 

where G is the gravitational 

constant, M is the mass of 

the body that is the source 

of the gravity, c is again the 

speed of light, and R is the 

distance from that same 

body. For Fig. 1, M is the 

mass of the Sun, and R is the 

distance of the spacecraft 

from the Sun. The gravitational 

effect of Venus was 

also examined but found to 

be negligible on the scale 

shown in the figure. The 

residual OCXO drift rate 

shown, the top curve in 

Fig. 1, is the result of subtracting 

both the gravitational 

effect and the velocity 

390 

Frequency offset (clock drift rate) (ppb) 

35 

30 

25 

20 

15 

10 

5 

Actual MET drift rate 

MET drift rate minus velocity effect 

Spacecraft velocity 

0 

0 

960 970 980 990 1000 1010 1020 1030 1040 1050 


Figure 2. MESSENGER OCXO-B behavior after March 2007 turn-on, with relativistic velocity effect 

removed. 

Fractional frequency offset (clock drift rate) (ppb) 

15 

10 

5 

0 

–5 

–10 

–15 

–20 

effect from the observed data. The variation of residual 

frequency offset from 31.0 ppb to 30.4 ppb over 70 days 

is reasonable and can be explained by a combination of 

temperature effects and oscillator frequency aging. 

This tells us that, after removal of the relativistic 

effects, the OCXO was running fast by approximately 

30–31 ppb, approximately 2.6–2.7 ms/day. 

TDTRATE AND THE MERCURY FLYBYS 

After the 2007 flyby of Venus, the MESSENGER 

spacecraft flew past Mercury three times and then, in 

a fourth encounter, went into orbit around Mercury. 

From the Venus flyby, we were able to infer from the 

Estimated OCXO-B frequency 

offset with relativistic effects 

Estimated TDTRATE with 

relativistic effects 

–25 

0.99999998500 

1220 1240 1260 1280 1300 1320 1340 1360 


JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 32, NUMBER 1 (2013) 

50 

45 

40 

35 

30 

25 

20 

15 

10 

5 

1.00000002500 

1.00000002000 

1.00000001500 

1.00000001000 

1.00000000500 

1.00000000000 

0.99999999500 

0.99999999000 

Figure 3. Estimated MESSENGER OCXO-B fractional frequency offset and TDTRATE during M1 due 

to relativity, assuming +31 ppb offset without relativity. 

Spacecraft velocity (km/s) 

TDTRATE (s/s)

ehavior of the MET counter 

how the OCXO behaved. We 

also determined that, with 

relativistic effects removed, 

the OCXO was running fast, 

that is, the OCXO output frequency 

was higher than the 

nominal design frequency. 

Prior to the first encounter 

with Mercury (M1), we 

reversed that process and, 

with the assumption that the 

OCXO was still running fast 

by the amount determined 

from the Venus data, derived 

the expected behavior of 

the OCXO and of the MET 

counter. That result is shown 

in Fig. 3, calculated using 

spacecraft velocity relative to 

the Sun and the gravitational effects of both the Sun 

and Mercury. One curve is the OCXO output frequency 

and equivalent clock drift rate expressed in parts per 

billion. Note how the oscillator and clock slowed down 

as solar perihelion was approached. The other curve 

expresses the clock behavior in terms of the parameter 

TDTRATE, an important metric of interest to Mission 

Operations Center staff. Note that the observations of 

clock behavior during the 2007 Venus flyby were actually 

observations of TDTRATE that were converted 

to the equivalent oscillator frequency offset behavior 

shown in Figs. 1 and 2. 

TDTRATE is obtained from the Operations SCLK 

Kernel. The Jet Propulsion Laboratory’s Navigation and 

Ancillary Information Facility (NAIF) provides to APL 

and to other users a suite of 

software and information 

system tools called Spacecraft 

Planet Instruments C-matrix 

Events (SPICE), designed to 

provide access to information 

about space missions. 

One component of SPICE is 

a set of “kernels” or parameter 

files that contain information 

relative to specific missions 

or to space missions in general. 

For example, ephemerides 

kernels might provide 

the ephemerides of planets 

or of specific spacecraft. One 

type of SPICE kernel is the 

SCLK kernel, a text file that 

provides mappings between 

MET and Earth time. Each 

time record of the SPICE 

TDTRATE (s/s) 

1.00000003000 

1.00000002500 

1.00000002000 

1.00000001500 

1.00000001000 

1.00000000500 

1.00000000000 

0.99999999500 

0.99999999000 

AN APPLICATION OF RELATIVITY TO SPACE MISSION TIMEKEEPING 

Estimated TDTRATE with 

relativistic effects 

Measured interpolated 

TDTRATE 

0.99999998500 

1220 1240 1260 1280 1300 1320 1340 1360 


Figure 4. Estimated MESSENGER OCXO-B TDTRATE during M1 due to relativity, assuming 

+31 ppb OCXO fractional frequency offset without relativity, compared with actual TDTRATE. 

TDTRATE (s/s) 

1.00000003000 

1.00000002500 

1.00000002000 

1.00000001500 

1.00000001000 

1.00000000500 

1.00000000000 

0.99999999500 

0.99999999000 

0.99999998500 

0.99999998000 

SCLK kernel contains three fields: (1) a field equivalent 

to MET, (2) a field representing Earth time, and (3) 

a clock change rate. At APL, our SCLK kernels have 

always expressed Earth time in the TT time system (previously 

abbreviated TDT), and we have typically called 

the clock change rate TDTRATE. 

The standard JPL SPICE SCLK kernel defines the 

clock change rate as a rate to be used to extrapolate the 

current MET–TT mapping to future times. At APL, we 

describe that rate as a “predicted TDTRATE.” Predicted 

TDTRATE is used, for example, in predicting the future 

time of execution of a command and is used to provide 

real-time estimates of time to the G&C subsystem. 

However, the APL-defined Operations SCLK Kernel 

takes that a step further and recalculates TDTRATE 

V2 is second Venus yby 

M1 is rst Mercury yby 

M2 is second Mercury yby 

M3 is third Mercury yby 

MOI is Mercury orbit insertion 

Estimated TDTRATE with relativistic effects 

Measured TDTRATE 

0 500 1000 1500 2000 2500 3000 


JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 32, NUMBER 1 (2013) 391 

V2 

M1 

M2 

M3 MOI 

Figure 5. Estimated MESSENGER OCXO-B TDTRATE, including the effects of relativity, assuming 

+28 ppb OCXO fractional frequency offset without relativity, using orbit determination solution 

OD153.

S. B. COOPER 

for past times to provide 

a more accurate mapping 

between MET and TT. That 

improved mapping is needed 

to provide the time accuracy 

required for analysis of 

science observations. That 

interpolated TDTRATE is 

shown in Fig. 3. The interpolated 

TDTRATE is based on 

both the current time record 

in the SCLK kernel and on 

the next time record, so the 

computed TDTRATE and 

derived oscillator frequency 

“lead” the actual performance 

of the oscillator. That 

is why the change in oscillator 

frequency shown in Fig. 2 

appears to occur slightly 

before the actual change in spacecraft velocity during 

the Venus flyby. 

A comparison between the interpolated TDTRATE 

taken from the Operations SCLK Kernel after the M1 

flyby and the relativistic prediction of TDTRATE given 

in Fig. 3 is shown in Fig. 4. The comparison is fairly good 

but not perfect and suggested that the +31 ppb OCXO 

fractional frequency offset of the Venus flyby might need 

to be adjusted. 

Analysis of TDTRATE following the second flyby of 

Mercury (M2) provided a better fit of +28 ppb to the 

M1 and M2 data, after relativistic effects were removed. 

However, that same analysis did not provide a good fit 

to the Venus flyby data, as can be seen in Fig. 5. The 

results shown in this figure provided the first prediction 

of OCXO TDTRATE through the end of the primary 

orbital phase of the mission, following a full Earth year 

in orbit around Mercury, and was 

calculated using spacecraft velocity 

relative to the Sun and the 

gravitational effects of the Sun, 

Earth, Venus, and Mercury. The 

gravitational effect of distant Jupiter 

is insignificant at this scale. 

This figure was created using an 

orbit determination designated 

OD153 by our Navigation Team 

at KinetX, as noted in the figure; 

later orbit determinations were 

used for the later figures. Note 

that TDTRATE has local maxima 

at solar perihelia, indicating that 

the OCXO output frequency and 

the clock drift rate have local 

minima near perihelia. Similarly, 

TDTRATE has local minima at 

392 

TDTRATE (s/s) 

1.00000003000 

1.00000002500 

1.00000002000 

1.00000001500 

1.00000001000 

1.00000000500 

1.00000000000 

0.99999999500 

0.99999999000 

0.99999998500 






V2 

M1 M2 M3 MOI 



0.99999998000 

0 500 1000 1500 2000 2500 3000 



+26 ppb OCXO fractional frequency offset without relativity, using orbit determination solution 

OD179. 

Residual fractional frequency 

offset (ppb) 

35 

30 

25 

20 

15 

10 

5 

aphelia, and the OCXO frequency and clock drift rate 

have local maxima at aphelia. In other words, the clock 

is running slower at perihelia (larger TDTRATE) and 

faster at aphelia (smaller TDTRATE), due to the relativistic 

effects of velocity and gravity. 

THE USE OF RELATIVITY TO CONTROL 

ONBOARD TIME 

It was noted earlier that the onboard G&C subsystem 

uses an estimate of Earth time. At various times, the 

Mission Operations Center uploads new time parameters 

to the spacecraft to allow the G&C subsystem to 

compute an accurate estimate of TT from MET. One of 

those parameters is a recently calculated value of predicted 

TDTRATE. Figure 5 and the calculations underlying 

the predictions of TDTRATE in that figure were 

Y = (–0.0043 ppb/day)X + 35.10 ppb 

Fractional frequency offset residual (ppb) 

to t measured TDTRATE 

Computed OCXO-B frequency bias, 

adjusted for aging (ppb) 

0 0 500 1000 1500 2000 2500 3000 


Figure 7. First linear fit to residual OCXO-B fractional frequency offset. 


provided to James Hudson of the 

MESSENGER Mission Operations 

Center in April 2009. As 

described by Hudson and Colwell, 

2 the Mission Operations 

Team used that information to 

create a model to determine an 

optimal value of TDTRATE to 

use onboard for the third Mercury 

flyby (M3) a few months 

later. The success of that process 

is shown in Fig. 5 of Ref. 2. 

Although relativistic corrections 

had been used for spacecraft 

before, such as for the GPS 

constellation, 3 this was a significant 

event for APL, perhaps the 

first time that a relativistic prediction 

had been used to control 

the accuracy of time onboard an 

APL spacecraft. 

NEW INSIGHTS INTO OSCILLATOR BEHAVIOR 

The apparent change in fractional frequency offset 

from the second Venus flyby (Fig. 1) to the second Mercury 

flyby (Fig. 5) suggested that the precision oscillator 

(OCXO) might be slowing down. That trend continued 

through the third Mercury flyby in September 2009; see 

Fig. 6. At that point, the characteristics of aging of that 

particular oscillator were not known other than the prelaunch 

vendor estimate of less than ±0.05 ppb/day for 

normal oscillator aging exclusive of any radiation effects. 

Using available values of interpolated 

TDTRATE taken from 

the Operations SCLK Kernel 

for times near eight solar perihelia, 

as shown in Fig. 6, the 

relativistic effects were removed 

and a linear least squares fit 

was applied to those residuals, 

shown in Fig. 7. This procedure 

gave an estimated average aging 

rate of −0.0043 ppb/day, much 

better than expected from the 

vendor’s estimate. 

The linear least squares fit 

of Fig. 7 was applied to the 

data of Fig. 6 to yield a prediction 

of TDTRATE with linear 

aging, which is shown in Fig. 8. 

With that estimate of OCXO 

aging, the relativistic prediction 

of TDTRATE “snapped into 

focus.” Over the following year, 

the performance of this estimate 

1.00000002500 

1.00000002000 

1.00000001500 

1.00000001000 

1.00000000500 

1.00000000000 

TDTRATE (s/s) 1.00000003000 

0.99999999500 

0.99999999000 

0.99999998500 

0.99999998000 






AN APPLICATION OF RELATIVITY TO SPACE MISSION TIMEKEEPING 



0 500 1000 1500 2000 2500 3000 


continued to be monitored (and the results provided 

to the Mission Operations Team), but the same linear 

least squares fit continued to be applicable. The OCXO 

fractional frequency offsets corresponding to Fig. 8 are 

shown in Fig. 9. All the flybys occurred at perihelia, 

where the oscillator frequency was lower and the clock 

was running slower. 

Near the end of the primary orbital phase of the mission 

in March 2012, a new linear least squares fit was 

made using only TDTRATE observations from the one 

year in orbit from March 2011 to March 2012, and the 

results were provided to the Mission Operations Team 

to support maintenance of onboard G&C time for 

JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 32, NUMBER 1 (2013) 393 

V2 


−0.0043 ppb/day OCXO linear frequency aging, using orbit determination solution OD179. 

Fractional frequency offset (ppb) 

15 

10 

5 

0 

–5 

–10 

–15 

–20 

–25 

–30 

Estimated OCXO-B 

frequency offset 

with relativistic effects, 

adjusted for aging (ppb) 

V2 

OCXO-B fractional frequency 

offset (ppb) from measured 

TDTRATE 

M1 

M1 

–35 

0 500 1000 1500 2000 2500 3000 


M2 

M2 

M3 

M3 

MOI 






Figure 9. Estimated MESSENGER OCXO-B fractional frequency offset, including the effects of 

relativity, assuming −0.0043 ppb/day linear frequency aging, using orbit determination solution 

OD179. 

MOI

S. B. COOPER 

OCXO frequency residual (ppb) 

35 

30 

25 

20 

15 

10 

5 

the extended mission that began on 18 March 2012. 

The results were somewhat surprising. The residuals 

(Fig. 10) again exhibited OCXO aging at a linear rate of 

−0.0043 ppb/day, but the linear fit was offset by almost 

−0.8 ppb from the earlier linear fit of cruise residuals 

(Fig. 7). Although it remains unclear, even after examination 

of additional data, whether the change in OCXO 

frequency was sudden or gradual, it appears likely that 

the increased OCXO temperature in orbit, shown in 

Fig. 10, accounts for at least part of the 0.8-ppb shift. 

CONCLUSIONS 

We’ve observed that the behavior of the MESSEN- 

GER precision oscillator, an OCXO, and the behavior 

of the clock driven by that oscillator are strongly 

influenced by relativistic effects due to the dynamics 

of the spacecraft trajectory. We successfully employed 

that observation to predict the future behavior of the 

onboard clock. The MESSENGER Mission Operations 

Team has incorporated that information into routine 

operations in determining the parameters needed to 

compute onboard G&C time. This has resulted in an 

The Author 

394 

Early cruise residuals 

On-orbit residuals 

88-day average OCXO-B temp. 

Fit to early cruise residuals 

Fit to on-orbit residuals 

Y = (–0.0043 ppb/day)X + 35.10 ppb 

Y = (–0.0043 ppb/day)X + 34.31 ppb 

OCXO-B temperature 

0 0 

0 500 1000 1500 2000 2500 3000 


Figure 10. OCXO-B fractional frequency residuals for last 5 years of the MESSENGER primary 

mission, after correction for relativistic effects, using orbit determination solution OD260. 

improvement in operator control 

of the error in G&C time. 

It was also determined, using 

knowledge of these relativistic 

effects, that the OCXO ages 

approximately linearly when the 

average oscillator temperature is 

fairly steady and that a linear fit 

to TDTRATE residuals provides a 

good prediction of future oscillator 

and onboard clock behavior. 

ACKNOWLEDGMENTS: I am grateful to 

the entire MESSENGER team for its 

support of the definition, development, 

and operation of the mission 

timekeeping system. The performance 

of this very accurate timekeeping 

system has made possible 

the observations described in this article. Jack Ercol and 

Allan Holtzman provided the oscillator temperature data 

used in this discussion. James Hudson and Edwin Colwell 

have handled the day-to-day operation of the timekeeping 

system and have embraced this new approach 

of using predictions of relativity to control the error in 

onboard G&C time. The MESSENGER Trajectory Database 

developed by James McAdams was used extensively 

to obtain the spacecraft velocity and ranges needed to 

compute the relativistic effects described. I’ve particularly 

enjoyed occasional chats with Robert Henderson about 

relativity and how it should be applied to this complex 

mission. Finally, I am indebted to Robert Jensen for his 

guidance on how to compute the relativistic effects of 

velocity and gravity on oscillator behavior. 

REFERENCES 

1 Cooper, S. B., “From Mercury to Pluto: A Common Approach to Mission 

Timekeeping,” IEEE Aerosp. Electron. Syst. Mag. 21(10), 18–23 (2006). 

2 Hudson, J. F., and Colwell, E. J., “Spacecraft Clock Maintenance for 

MESSENGER Operations,” in Proc. AIAA SPACE 2011 Conf. and 

Exposition, Long Beach, CA, paper AIAA 2011-7183. 

3 Parkinson, B. W., and Spilker, J. J. Jr. (eds.), Global Positioning System: 

Theory and Applications, Vol. 1, American Institute of Aeronautics & 

Astronautics, Inc., pp. 678–679 (1996). 

Stanley B. Cooper is an electrical engineer in the Space Department’s Mission Design, Guidance and Control Group 

(SEG) and is a member of the Senior Professional Staff. For the past decade, he has been responsible for the mission timekeeping 

systems for a variety of space missions. He previously designed flight and ground electronics and ground software 

for a variety of APL projects for spacecraft, shipboard, and laboratory use. His e-mail address is stanley.b.cooper@jhuapl.edu. 

The Johns Hopkins APL Technical Digest can be accessed electronically at www.jhuapl.edu/techdigest. 

70 

60 

50 

40 

30 

20 

10 

OCXO temperature (ºC)

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